On optimal monetary policy and the Taylor Rule in a New Keynesian Model

Abstract

Recently, many economists and some Republican members of Congress have targeted FED, arguing that the Central Bank of United States of America needs to adopt the Taylor interest rate rule instead of being totally free to conduct monetary policy. In this study, we try to analyze the stabilizing role of monetary policy in a new-Keynesian dynamic general equilibrium model in which there exist Calvo type price fixities. The new-Keynesian model, unlike the neoclassical one, could explain the monetary cycles, i.e. the economic fluctuations caused by monetary disturbances. These shocks are transmitted in real terms by the stepwise adjustment of price levels. Moreover, we derive and analyze optimal monetary policy and emphasize the properties of the optimal monetary policy rule. More specifically, we discern two cases. Fist, we assume that the monetary authorities can perfectly handle inflation and we show that the optimal policy is first best, since the monetary authorities, by using as instrument the inflation rate, can attain two linearly independent targets: the stabilization of inflation and the stabilization of the welfare-relevant output gap. In other words, the divine coincidence, noted by Blanchard and Gali (2007) for the standard New Keynesian Model, is perfect applied in this model. In addition, we demonstrate that the optimal policy can be replicated by a set of appropriately parameterized Taylor rules. We prove that the optimal Taylor rule is not unique, as multiple sets of parameters are consistent with optimality. Also, we prove that the optimal policy could be replicated through a unique, appropriately parametrized Wicksell rule, according to which deviations of the nominal interest rate from its “natural” rate depend only on deviations of inflation from target. Second, we assume that the monetary authorities can imperfectly handle inflation and we conclude that optimal monetary policy is second best and can be replicated by a set of appropriately parameterized Wicksell rules and by a set of appropriately parameterized Taylor rules. We prove that the optimal Taylor rule is not unique, as multiple sets of parameters are consistent with optimality and that the Wicksell rule has two possible parameters which are consistent with optimality. Finally, we focus on the fact that New-Keynesian models do not satisfy the "natural rate property", and we suggest an effective confrontation for this problem.